Daniel H. Gottlieb

Abstract

Let M be a manifold, with or
without boundary, which is dominated by a finite complex. Let G be a finite group
which acts faithfully and freely on M. Let f : M → M be a G-map. Let Λf denote
the Lefschetz number of f and let o(G) denote the order of G. The main result
states, under the conditions above, that o(G) divides Λf. Even in the case
of compact M this result was not widely known. We use Wall’s finiteness
obstruction theory to extend the result from compact M to finitely dominated
M.